Supersymmetric benchmarks with non-universal scalar masses or gravitino dark matter

We motivate, propose and examine a new set of benchmark supersymmetric scenarios, some of which have non-universal Higgs scalar masses (NUHM) and others have gravitino dark matter (GDM). The scalar masses in these proposed models are either considerably larger or smaller than the narrow range allowed for the same gaugino mass m(1/2) in the constrained MSSM (CMSSM) with universal scalar masses m(0) and neutralino dark matter. Unlike the CMSSM, the proposed NUHM and GDM models with larger m(0) may have large branching ratios for Higgs and/or Z production in the cascade decays of heavier sparticles, whose detection we discuss. The novel phenomenology of the GDM models depends on the nature of the next-to-lightest supersymmetric particle (NLSP), which has a lifetime exceeding 10(4) s in the proposed benchmark scenarios. In one GDM scenario the NLSP is the lightest neutralino chi, and the supersymmetric collider signatures are similar to those in previous CMSSM benchmarks, but with a distinctive spectrum that would be challenging for the LHC and ILC. In the other GDM scenarios based on minimal supergravity (mSUGRA), the NLSP is the lighter stau slepton (tau) over tilde (1), with a lifetime between similar to 10(4) and 3 x 10(6) s. Every supersymmetric cascade would end in a (tau) over tilde (1), which would have a distinctive time-of-flight signature. Slow-moving (tau) over tilde (1)'s might be trapped in a collider detector or outside it, and the preferred detection strategy would depend on the (tau) over tilde (1) lifetime. We discuss the extent to which these mSUGRA GDM scenarios could be distinguished from gauge-mediated models.